In certain data communications systems, demodulation of received data signals is hindered by data carrier frequency uncertainty. For example, in mobile satellite communications systems the land mobile demodulators must be able to lock on to intermittent data signals masked by high levels of noise. In such systems, carrier frequency changes due to oscillator drift or to Doppler shift from user movements can be a significant fraction of the data rate. Thus, it is an important characteristic of a demodulator in the land mobile satellite system to be able to identify and to lock on to the data carrier frequency in the presence of high noise, shadowing, multipath fading, oscillator drift, and Doppler shift.
Another problem confronting a land mobile demodulator in a satellite communications system is that the phase modulated data signal appears as a double peak amid the background noise with the actual carrier frequency falling between the peaks. In prior art systems that use fine grain transforms to find the data signal, one or the other of the double peaks can be selected as the carrier frequency rather than the actual carrier frequency that falls between the peaks.
It is also known in the prior art that the double peaks of the data signal can be eliminated by squaring the signal. Squaring results in a single peaked signal that can be analyzed using the fine grain transform described above. However, squaring the signal doubles the frequency and the bandwidth and increases the noise. Furthermore, squaring the signal requires a higher sampling rate along with the inherent computational difficulties of dealing with the doubled bandwidth.
Thus, there is a need for a method of finding and approximating the carrier frequency of a data signal having a very low signal-to-noise ratio in a wide search bandwidth. Furthermore, it is desirable that the method provide the approximate carrier frequency rapidly and in a computationally efficient manner. Determining the approximate carrier frequency is important as the first step in narrowing the bandwidth to provide a higher signal-to-noise ratio and to provide a starting frequency for a frequency-locked loop in a demodulator.